Suppose and is negative. Here are some small variations on the previous problems:
Can someone please point me in a direction towards solving this problem, I am not sure what they are asking?
$\displaystyle \cos{u} > 0$ and $\displaystyle \sin{u} < 0$ indicates $\displaystyle u$ is a quad IV angle.
$\displaystyle \cos{u} = \frac{5}{13} \, , \, \sin{u} = -\frac{12}{13}$
to calculate the rest, use the difference identity for sine and cosine ...
$\displaystyle \sin(a - b) = \sin{a}\cos{b} - \cos{a}\sin{b}$
$\displaystyle \cos(a-b) = \cos{a}\cos{b} + \sin{a}\sin{b}$
You can also note that a right triangle with hypotenuse of length 13 and one leg of length 5 has cosine of the angle between those two side 5/13. What is the length of the other leg? And from that, what is the sine of the angle? This is treating the angle as between 0 and $\displaystyle \pi/2$. Use the quadrant information to find the sign.